Transformations on Parent Functions

Given the function  $y=\left(x+4\right)^2+2$  , what is the parent function?

•  $y=x^2$  

•  $y=a\left(x-h\right)^2+k$  

•  $y=mx+b$  

•  $y=0\left(x-0\right)^2+0$  

Tags

CCSS.HSF.IF.C.7

 $y=\sqrt{x-\frac{3}{2}}+2$  belongs to what family of functions?

• square root

• absolute value

• linear

• quadratic

Write the equation that results if the parent absolute value function is shifted right 15 units, down 3 units, and reflected vertically.

• $y=-\left|x-15\right|-3$

• $y=-\left|x+15\right|-3$

• $y=\frac{1}{2}\left|x+3\right|-15$

• $y=\frac{1}{2}\left|x-3\right|-15$

• $y=\left|-x-15\right|-3$

Tags

CCSS.HSF.BF.B.3

Where is the vertex of  $y=3\left(x-26\right)^2+14$  ?

• (26, 14)

• (14, 26)

• (-26, 14)

• (3, 14)

• (3, 26)

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

In the image, what is the value of the maximum?

• $y=8$

• $x=-2$

• $\left(-2,8\right)$

• There is no maximum value

Tags

CCSS.HSA.REI.D.10

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

Since the equations of vertical lines always have the form  $x=a$  for some constant a, what is the equation for the line of symmetry of the pictured graph?

•  $x=1$  

•  $y=1$  

•  $x=-2$  

•  $y=0$  

Tags

CCSS.HSA.CED.A.2

CCSS.HSA.REI.D.10

Which transformations are involved in the equation  $y=\frac{1}{2}\sqrt{x+1}-1$  ?

• Horizontal translation left

• Vertical shrink

• Vertical translation down

• Horizontal translation right

• Vertical stretch

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2

If  $f\left(x\right)=a\left(x-h\right)^2+k$  has a horiz. shift of -2, a vertical shift of +3 and a vertical stretch of 4, what are the values of a, h, and k?

•  $a=4;\ h=-2;\ k=3$  

•  $a=2;\ h=4;\ k=-3$  

•  $a=4;\ h=2;\ k=3$  

•  $a=3;\ h=2;\ k=-4$  

Tags

CCSS.HSF.BF.B.3

If  $f\left(x\right)=a\left(x-h\right)^2+k$  has a horiz. shift of -2, a vert. shift of 3 and a vert. stretch of 4, what is the equation for  $f\left(x\right)$  ?

•  $f\left(x\right)=4\left(x+2\right)^2+3$  

•  $f\left(x\right)=4\left(x-2\right)^2+3$  

•  $f\left(x\right)=3\left(x+2\right)^2+4$  

•  $f\left(x\right)=2\left(x-4\right)^2+3$  

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.2

CCSS.HSF.BF.B.3

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

What does the transformation $f\left(x\right)\ \rightarrow\ f\left(x+1\right)-9$ do to the graph of  $f\left(x\right)$  ?

• translates it left one unit and down 9 units

• translates it right one unit and down 9 units

• translates it up one unit and right 9 units

• translates it down one unit and left 9 units

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2